81.14.21 problem 18-34

Internal problem ID [21706]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 18. Algebra of differential operators. Page 435
Problem number : 18-34
Date solved : Thursday, October 02, 2025 at 08:00:10 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}+y^{\prime \prime }&=x^{5}-3 x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 67

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+diff(diff(y(x),x),x) = x^5-3*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{\frac {x}{2}} \left (c_3 \sqrt {3}+c_2 \right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )}{2}+\frac {{\mathrm e}^{\frac {x}{2}} \left (c_2 \sqrt {3}-c_3 \right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )}{2}+\frac {x^{7}}{42}-\frac {21 x^{4}}{4}+c_4 x +c_1 \,{\mathrm e}^{-x}+c_5 \]

✓ Mathematica. Time used: 0.28 (sec). Leaf size: 101

ode=D[y[x],{x,5}]+D[y[x],{x,2}]==x^5-3*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^7}{42}-\frac {21 x^4}{4}+c_5 x+c_1 e^{-x}-\frac {1}{2} \left (\sqrt {3} c_2+c_3\right ) e^{x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )-\frac {1}{2} \left (c_2-\sqrt {3} c_3\right ) e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+c_4 \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 53

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**5 + 3*x**2 + Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{5} e^{- x} + \frac {x^{7}}{42} - \frac {21 x^{4}}{4} + \left (C_{3} \sin {\left (\frac {\sqrt {3} x}{2} \right )} + C_{4} \cos {\left (\frac {\sqrt {3} x}{2} \right )}\right ) e^{\frac {x}{2}} \]